Quantile of a Mixture
Carole Bernard, Steven Vanduffel

TL;DR
This paper derives an explicit formula for the quantile of a mixture of two random variables, aiding in risk assessment when limited information is available.
Contribution
It provides a comprehensive analysis of the quantile of mixtures, including discrete and continuous cases with unbounded support, enhancing risk management tools.
Findings
Explicit formula for mixture quantiles derived
Applicable to discrete and continuous variables with unbounded support
Facilitates bounds on Value-at-Risk with partial information
Abstract
In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for finding bounds on the Value-at-Risk of risky portfolios when only partial information is available (Bernard and Vanduffel (2014)).
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Taxonomy
TopicsProcess Optimization and Integration
